Granted, it's safer to come in the night before, but you have to look at the total picture...
Are you flying on a non-stop from one city? Or are there legs? Who is your airline? If you are non-stop, are you the first flight out that morning or does the plane need to arrive from somewhere else first? What is the season? Will you be flying during snow season from a northern climate?
I believe you can check the on-time overall performance of most flights, just not sure how to do that, perhaps the FAA website. Also, if you want to change your flight, it never hurts to tell the agent why---a lot of times they will waive the change fee. If the agent says no, pass on it, and try a few times more---you might get lucky eventually.